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Equation 8 · Part 7 · How AI Datacenter Power and Cooling Actually Work

subscript

Q˙=m˙cpΔT\dot{Q} = \dot{m} c_p \Delta T
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Heat reuse imposes a real constraint back onto the cooling-loop design, and it is a direct consequence of the Q˙\dot{Q} = m˙\dot{m} cpc_p Δ\Delta T relation above: a district heating network needs delivery water above some useful temperature (often 60–90°C depending on the network), which is far above what a direct-to-chip loop returns on its own. A heat pump bridges that gap, but every heat pump has a coefficient of performance that degrades as the temperature lift it must perform increases — so a datacenter operator sizing for heat reuse has a genuine incentive to run its internal coolant loop at a higher return temperature than a pure cooling-efficiency design would choose, trading some…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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